In reply to Beimar Iriarte.

I do not know how to construct a confidence band for Deming regression. Traditional bands are prediction intervals and are constructed from residuals. But there are no residuals in this computation because X and Y are measured together and both contain measurement error. I don't think a "prediction interval" makes sense because you aren't using X to predict Y or vice versa. You are testing to see whether the two measurements are linearly related over a range of values.

I think the confidence intervals for the parameters answer the scientific question, which is "are these measurements linearly equivalent?" When they are on the same scale, that means testing the hypotheses that Intercept=0 and Slope=1. I guess you could use bootstrapping to visualize the uncertainty in the regression line. You would sample with replacement many times and compute the regression line for each bootstrap resample. Then overly the semitransparent lines. It would look similar to my article on visualizing uncertainty in regression models. See the graph in the section "Simulate from the fitted model." But, to be honest, I'd rather view a scatter plot of the bootstrap estimates and overlay reference lines at (Intercept, Slope) = (0, 1). I think the scatter plot is more informative and less likely to be misinterpreted.